Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal’s selection is 1/3 and that of Monika’s selection is 1/5. Find the probability that
i. Both of them will be selected
ii. None of them will be selected
iii. At least one of them will be selected
iv. Only one of them will be selected.
Given that,
⇒ P(KS) = P(Kamal’s selection)
⇒
⇒ P(KN) = P(Not selecting Kamal)
⇒
⇒
⇒ P(VS) = P(Monika’s selection)
⇒
⇒ P(VN) = P(Not selecting Monika)
⇒
⇒
We need to find:
i. Both of them will be selected
ii. None of them will be selected
iii. At least one of them will be selected
iv. Only one of them will be selected.
⇒ P(Sboth) = P(Both of them are selected)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
⇒ P(Snone) = P(None of them are selected)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
⇒ P(Satone) = P(Selecting at least one of them)
⇒ P(Satone) = P(selecting only Kamal) + P(selecting only Monika) + P(Selecting both)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
⇒
⇒ P(Sone) = P(Only one of them is selected)
⇒ P(Sone) = P(only Kamal is selected) + P(only Monika is selected)
Since selection of each person is an independent event their probabilities multiply each other
⇒
⇒
⇒
∴ The required probabilities are .